Progressive power ophthalmic lens

ABSTRACT

An improved ophthalmic lens for presbyopia is disclosed in which the refractive power is progressively changed to provide a natural visual target arrangement. In the .[.opthalmic.]. .Iadd.ophthalmic .Iaddend.lens, rotation of the head of a wearer for binocular lateral vision is taken into account to permit comfortable binocular lateral vision closer to vision with the naked eyes.

This invention relates to .[.opthalimic.]. .Iadd.ophthalmic.Iaddend.lenses and more particularly to improvements in an ophthalmiclens for presbyopia having progressively changing refractive power.

Presbyopia designates such a state of the eyes of a man that the eyelens in the eyeball is no more capable of adjusting itself to focusingnecessary for near vision due to the loss of its original elasticity.Therefore, he will be able to easily see an object located at a shortdistance again when he wears a convex lens which makes up the shortageof accommodation.

It is customary that near vision is generally done through the lowerareas of lenses mounted in a spectacle frame. Therefore, a single pairof spectacles can make necessary visual power compensations for both thenear vision and the distant vision when the lower areas of theconventional lenses for distant vision in the spectacle frame arereplaced by the convex lenses described above.

A bifocal lens is a simplest form of such a multifocal ophthalmic lens.The convex lens portion for near vision in the multifocal ophthalmiclens is called the segment, and there are a variety of kinds in theshape, location, material, etc. of the segment.

However, the lenses of this kind have had such a common defect that,during transition of vision from distant vision to near vision, thereoccurs an abrupt change in the magnification resulting in a sense ofphysical confusion. A so-called progressive power .[.opthalmic.]..Iadd.ophthalmic .Iaddend.lens has been proposed in an effort toalleviate the abrupt change in the magnification of the image. Accordingto the progressive power ophthalmic lens, the surface design is suchthat the refractive power is progressively changed to eliminate thesense of physical confusion, and the field of intermediate vision canalso be provided in the region of the boundary between the distantvision and the near vision.

This progressive power .[.opthalmic.]. .Iadd.ophthalmic .Iaddend.lens isalso aesthetically advantageous over the bifocal lens in that theboundary line separating the lens portion for near vision is notconspicuously sensed in the external appearance compared with thebifocal lens, and, thus, it is not perceived as that specificallyprepared for presbyopia.

The progressive power ophthalmic lens is featured by the presence of asuccession of "umbilical points" forming a so-called "umbilical meridiancurve" extending substantially from an upper central portion to a lowercentral portion of the lens surface. This "umbilical meridian curve" issuch that astigmatism therealong is almost equal to zero, and therefractive power changes progressively according to a predeterminedrule. The term "umbilical point" is used herein to designate the pointat which two major radii of curvature are equal to each other.

A lens surface having such an "umbilical meridian curve" can betheoretically relatively easily designed as will be described later.

However, in the prior art progressive power ophthalmic lens, therotation of the head of a wearer for lateral vision described later isnot utterly taken into account. Generally, it is customary that not onlythe eyeball but also the head of a wearer is turned toward a visualtarget located on a lateral side when the wearer sees such a visualtarget. In other words, the rotation of the head compensates for therotation of the eyeball. In the case of the prior art progressive powerophthalmic lens, the arrangement of the visual target, which was assumedby a designer when he designs a lens, has been unnatural because of thefact that the rotation of the head is not utterly taken into account.

It is therefore a primary object of the present invention to provide anophthalmic lens in which the unnatural arrangement of the visual targetin the prior art lens is replaced by a more natural visual targetarrangement, and the rotation of the head of the wearer for binocularlateral vision is taken into account, thereby permitting comfortable.[.bimocular.]. .Iadd.binocular .Iaddend.lateral vision quite close tothe vision with the naked eyes.

In accordance with the present invention, there is provided anophthalmic lens having two refractive surfaces, one of the refractivesurfaces including an imaginary first meridian curve called, for thepurpose of explanation, an umbilical meridian curve extendingsubstantially in the vertical direction along the refractive surfacewhen the refractive surface is viewed from a direction substantiallyorthogonal with respect thereto in the condition in which the lensstands in the same vertical direction as that mounted on a wearer, thedistribution of the radius of curvature of the umbilical meridian curveincluding a zone in which the radius of curvature decreases graduallyfrom an upper portion toward a lower portion of the curve according to apredetermined rule, the radii of curvature at the intersections oforthogonal curves crossing at right angles with the umbilical meridiancurve in the refractive surface being substantially equal to the radiiof curvature of the umbilical meridian curve at those intersectionsrespectively so that the astigmatism along the umbilical meridian curvein the refractive surface is almost equal to zero, the umbilicalmeridian curve dividing the refractive surface into two lateral areascloser to the nasal side and temporal side respectively when the lens ismounted on the wearer, the two lateral areas of the refractive surfacebeing asymmetrical with each other, the refractive surface being suchthat, when a second meridian curve extending in the vertical directionalong the refractive surface to overlap, intersect or contact with theumbilical meridian curve in an upper region of the refractive surface isimagined, the umbilical meridian curve is displaced toward the nasalside relative to the second meridian curve in a lower region of therefractive surface, while it is .[.less.]. gradually displaced towardthe nasal side relative to the second meridian curve in an intermediateregion of the refractive surface, the intermediate and lower regions inwhich the umbilical meridian curve is displaced more or less toward thenasal side relative to the second meridian curve including at least onesectional curve which extends in the horizontal direction within a rangeof not more than 15 mm on opposite sides of the umbilical meridian curveand along which the distribution of astigmatism on the nasal siderelative to the umbilical meridian curve is asymmetrical with that onthe temporal side.

Other objects, features and advantages of the present invention willbecome apparent from the following detailed description of preferredembodiments thereof taken in conjunction with the accompanying drawings,in which:

FIG. 1 is a diagrammatic view illustrating a general method of designinga lens surface having progressingly changing refractive power;

FIG. 2 is a diagrammatic view illustrating the position of a visualtarget in the prior art;

FIG. 3 is a diagrammatic view illustrating the relation between thedirection of a visual target and the rotation of the head as well as theeyeball of the spectacle wearer, for explaining the principle of thepresent invention;

FIG. 4 is a diagrammatic view illustrating, by way of example, theposition of a visual target for the wearer wearing the ophthalmic lensaccording to the present invention;

FIG. 5 is a diagrammatic view also illustrating, by way of example, theposition of a visual target for the wearer wearing the ophthalmic lensaccording to the present invention;

FIG. 6 is a diagrammatic view illustrating, by way of example, the caseof binocular vision of the visual target shown in FIG. 5; and

FIG. 7 is a schematic elevational view showing one form of theprogressive power ophthalmic lens according to the present invention.

For a better understanding of the present invention, a general method ofdesigning a lens surface having progressively changing refractive powerwill be described with reference to FIG. 1, before describing thepresent invention in detail.

A plane Q called a principal vertical meridional plane hereinafter isfirst established in the space as shown in FIG. 1.

Then, on this principal vertical meridional plane Q, a helical curveM--M' called a meridian curve hereinafter is drawn which extends from anupper portion toward a lower portion of the plane Q and has its radiusof curvature continuously decreased from its upper portion to its lowerportion according to a predetermined rule. Subsequently, a plane Viincluding points Gi and Oi and crossing in orthogonal relation with theprincipal vertical meridional plane Q is established as shown in FIG. 1,where Ri is the radius of curvature of the meridian curve M--M' at aselected point Gi, and Oi is the center of curvature. This plane Vi iscalled an orthogonal plane hereinafter.

Then, on this orthogonal plane Vi, a curve Hi--Hi' is drawn which passesthrough the point Gi, whose radius of curvature at the point Gi is equalto the radius of curvature Ri above described, and whose center ofcurvature coincides with the point Oi above described. This curveHi--Hi' is called an orthogonal curve hereinafter. Such an orthogonalcurve Hi--Hi' can be drawn for all of the points on the meridian curveM--M', and, therefore, the group of such orthogonal curves Hi--Hi' formsa curved surface. Thus, when such a curved plane is employed to providea lens surface, any one of the points on the meridian curve M--M'provides an "umbilical point" at which the two major radii of curvatureare equal to each other. Consequently, the meridian curve M--M' providesan "umbilical meridian curve" along which the astigmatism is almostequal to zero.

In the above description, only one .[.orthogoanl.]. .Iadd.orthogonal.Iaddend.curve Hi--Hi' has been defined for the point Gi.

It is apparent, however, that any one of the curves having the sameradius of curvature Ri at this point Gi can be employed as theorthogonal curve Hi--Hi'. There are many examples having attempted toimprove the progressive power ophthalmic lens utilizing the degree offreedom of the orthogonal curve Hi--Hi', and the present invention isalso not an exception. These prior art examples include Japanese PatentPublication No. 3595/74, Japanese Patent Application Laid-open No.46348/75 and Japanese Patent Publication No. 9626/72. According to theinvention of Japanese Patent Publication No. 3595/74, the radius ofcurvature of the orthogonal curve Hi--Hi' is decreased from the centertoward the lateral sides in the upper portion of the lens and isincreased from the center toward the lateral sides in the lower portionof the lens, so that the overall astigmatism of the lens is consequentlydistributed or diluted over a wide range. According to the invention ofJapanese Patent Application Laid-open No. 46348/75, the major directionsof astigmatism in the side portions of the lens, that is, the directionsof image distortion are arrayed in the vertical and horizontaldirections of the side portions, thereby intending to alleviate ornullify the effect of astigmatism. However, there are very few examplesof inventions concerning binocular lateral vision occupying a very largeproportion of vision in the eneryday life, and, among the prior artexamples cited above, Japanese Patent Publication No. 9626/72 deals,only insufficiently, with the subject of binocular lateral vision. Theimportant feature of the last-mentioned patent publication resides inthe fact that astigmatic errors on a lens surface are made symmetricalin the horizontal direction on opposite sides of a meridian planeincluding an inclined umbilical meridian curve.

The lens for the right eye and the lens for the left eye are generallyin the form of mirror images of each other, that is, they are generallysymmetrical with each other relative to the nose. In the prior artexample disclosed in the last-mentioned patent publication, therefore,the angle of rotation of the eyeball of the right eye is regarded to beapproximately equal to that of the eyeball of the left eye when the eyesof the wearer are turned in a lateral direction from the conditiondirected toward the front. In this case, the intersection of the rightand left fixation lines, that is, the position of the visual target isrepresented by a point on a curve C shown in FIG. 2. This curve C is aportion of an arc in which the line connecting between the centers ofrotation O_(L) and O_(R) of the eyeballs of the left and right eyesrespectively provides the chord, and the angle of circumference of thechord is equal to the angle of vision α. However, such a visual targetarrangement is quite unnatural as a matter of course and does not in anyway reflect the usual condition of vision. Further, the illustratedvisual target arrangement is not fully sufficient or convincing in thatthe rotation of the head of the wearer for lateral vision describedlater is not utterly taken into account. Generally, it is usual that notonly the eyeballs but also the head is rotated toward a visual targetwhen we see a visual target disposed laterally relative to the front. Inother words, the head is rotated to compensate for the rotation of theeyeballs.

FIG. 3 illustrates that the wearer turns his eyes toward a visual targetdisposed laterally at an angle β relative to the front from thecondition seeing an object disposed directly in front of him. When theangle of rotation of the eyeballs relative to the head is designated byβ_(E), the relation β=β_(H) +β_(E) holds generally. If the visual targetdisposed in the direction of the angle β is very interesting for thewearer, the relation β_(H) >β_(E) would hold, and, in the contrary case,the relation β_(H) <β_(E) would hold. However, it may be sufficient thatthe relation therebetween is generally given by β_(H) ˜β_(E). Further,when the angle β is very large as when, for example, the visual targetis disposed in the rear of the wearer, the wearer will turn or twist hisbody or the wearer will change the direction of his legs to rotate thebody itself toward the rear. In such a case, the body and limbs of thewearer cooperate bodily, as the word implies, to assist in the effort ofthe eyeballs trying to see the visual target. The same applies when thevisual target is disposed in an upper or lower position besides thelateral position. By taking into account the above matter in the opticaldesign of ophthalmic lenses, a quite novel function not having beenproposed yet by the prior art ones can be developed so that comfortableophthalmic lenses permitting viewing of an object in a conditionanalogous to viewing with the naked eyes can be provided. It is thus theobject of the present invention to provide an ophthalmic lens which isbased upon the standpoint entirely different from that of the prior artones and which obviates all of the defects of the prior art ones.

More particularly, the present invention contemplates to provide anophthalmic lens in which the unnatural arrangement of the visual targetin the prior art ones is replaced by a more natural visual targetarrangement, and the rotation of the head of the wearer for binocularlateral vision is taken into account, thereby permitting comfortablebinocular lateral vision closer to vision with the naked eyes.

A practical aspect of the present invention will now be described indetail. As a first example, a straight line D as shown in FIG. 4 isselected to represent a most natural visual target arrangement in thehorizontal direction. In FIG. 4, the symbol O_(R) designates the centerof rotation of the eyeball of the right eye, and the symbol Podesignates the position of the visual target on the straight line D whenthe eyeball of the right eye is directed toward the front. Also, in FIG.4, the line O_(R) Po connecting between O_(R) and Po intersects at rightangles with the straight line D. The line O_(R) Po has a length a, andthe symbols P₁₀ to P₉₀ designate the successive positions of the visualtarget on the straight line D when the eyeball of the right eye isrotated successively through an angle of 10° at a time toward the rightfrom the front looking position. In view of the limited illustrationspace, the symbols P₇₀, P₈₀ and P₉₀ are put in parentheses, and thedirections of the positions P₇₀, P₈₀ and P₉₀ are merely shown by thearrows. Further, the position P₉₀ represents a point at infinity in theright direction.

Now, an arbitrary point Pi defining an angle >PoO_(R) Pi=β is selectedon the straight line D. Then, the distance O_(R) Pi between O_(R) and Piis expressed as O_(R) -Pi=α/cos β. As described hereinbefore, there isthe relation β=β_(H) +β_(E), where β_(H) represents the angle ofrotation of the head, and β_(E) represents the angle of rotation of theeyeball of the right eye relative to the head, when the wearer sees thevisual target disposed in the lateral position Pi angularly spaced apartby the angle β from the position Po. Consider now the position on theophthalmic lens through which the fixation line of the right eye passes.Then, the direction of the fixation line, that is, the direction of thevisual target is represented by the angle β_(E) and is not representedby the angle β for the ophthalmic lens itself. This is because theophthalmic lens and the head of the wearer are theoretically integralwith each other, and the angle β.sub. H of unitary rotation of theophthalmic lens and the wearer's head is entirely independent of thefixation line of the eyeball of the right eye relative to the ophthalmiclens. In other words, the direction of the visual target (represented bythe angle β) for the lens wearer himself is different from the directionof the visual target (represented by the angle β_(E)) for the ophthalmiclens itself, and the difference therebetween is equal to the angle ofrotation β_(H) of the head of the wearer. This is the most important.[.basis.]. .Iadd.basic .Iaddend.principle of the ophthalmic lens of thepresent invention which differs fundamentally from the prior art ones.Standing on the viewpoint above described, consider now the relativechange between the position of the visual target for the spectaclewearer himself, which position is shown on the straight line D in FIG.4, and the position of the visual target for the ophthalmic lens itself.Rotation of the wearer's head through the angle β_(H) relative to thevisual target means that the visual target rotates through an angle--β_(H) relative to the wearer's head, according to the relative way ofthinking. Suppose that all of the centers of rotation are located on thecenter of rotation O_(R) of the eyeball of the right eye shown in FIG. 5and there holds the relation β_(H) ˜β_(E) between the angles β_(H) andβ_(E). Then, the position Pi of the visual target for the lens wearerhimself, which position is arbitrarily selected on the straight line D,shifts to a position Pi' for the ophthalmic lens itself. The latterposition Pi' is determined by counter-clockwise rotation of the positionPi around the eyeball rotation center O_(R) through an angle β/2, asshown in FIG. 5. It will be seen in FIG. 5 that the relation O_(R)Pi=O_(R) Pi', holds, and the distance between the eyeball of the righteye and the visual target is unchanged. Thus, when a plurality of pointsP₁₀ ' to P₉₀ ' corresponding to the respective points P₁₀ to P₉₀ aresimilarly plotted, these points P₁₀ ' to P₉₀ ' form a curve D' as shownin FIG. 5. When the eyeball rotation center O_(R) in FIG. 5 is taken asan origin, and the lines extending rightward and upward from this originO_(R) in FIG. 5 are taken as the x-axis and y-axis respectively, the xand y coordinates of the point P_(i) ' on the curve D' are expressed asfollows: ##EQU1## Therefore, the curve D' in FIG. 5 is expressed asfollows: ##EQU2## Although the above description has referred only tothe case of rightward monocular vision by the right eye for simplicityof explanation, it is apparent that the same applies to leftwardmonocular vision by the right eye and also to lateral vision by the lefteye.

Further, although the center of rotation of the head is regarded tocoincide with the center of rotation of the eyeball in the abovedescription, it is needless to mention that the position of the formeris not the same as that of the latter.

In the case of binocular vision, the presence of the distance O_(R)O_(L) between the eyeballs of the right and left eyes shown in FIG. 6must be taken into account. It can therefore be readily surmised thatthe visual target for the pair of ophthalmic lenses will be representedby the combination of the curve D_(R) ' representing the visual.[.targer.]. .Iadd.target .Iaddend.for the right eye and the curve D_(L)' representing the visual target for the left eye, as shown in FIG. 6.

In the consideration of binocular vision, one of the eyes may bedominant over the other, that is, the "dominant eye" may be present. Insuch a case, it can be easily surmised that the effect of the positionof the visual target corresponding to the eyeball of the "dominant eye"will be greater than that of the position of the visual .[.targer.]..Iadd.target .Iaddend.viewed with binocular vision. However, it maygenerally suffice to consider that a curve D" lying intermediate betweenthe visual target curves D_(L) ' and D_(R) ' for the left and right eyesrespectively, as shown in FIG. 6, provides the position of the visualtarget in the case of binocular vision.

It is to be noted that this curve D" .[.differes.]. .Iadd.differs.Iaddend.greatly from the curve C in FIG. 2 showing the visual targetposition in the prior art ophthalmic lens.

In FIG. 6, a visual target Pi" is shown displaced rightward from thefront-viewing position Po on the curve D". As this visual target Pi"moves infinitely rightward from the position Po, the angle α" ofbinocular vision for viewing the visual target located at the positionPi", that is, the angle <O_(L) Pi"O_(R) approaches progressively tozero. This progressive approach of the angle of binocular vision towardzero means that the relative convergence of the two eyes approachesprogressively to zero. The angle of binocular vision attains finally thevalue of zero when β=90° or β_(E) =45° in the illustrated example. Insummary, the relative convergence of the two eyes continues toprogressively decrease as the lens wearer turns his eyes progressivelyin the lateral direction from the condition viewing a visual targetlocated at a finite distance in front of him, and the relativeconvergence is finally reduced to zero when the eyeballs of the eyes ofthe lens wearer are directed to view a visual target located in theextreme lateral direction in which β =90°, that is, when the ophthalmiclenses are directed to view a visual target located in the lateraldirection in which β_(E) is about 45°.

We will discuss the passing positions of the fixation lines on theophthalmic lenses, that is, the positions on the ophthalmic lensesthrough which the wearer views a visual target disposed in the lateraldirection.

Referring to FIG. 7, reference numerals 71 and 72 designate left andright ophthalmic lenses respectively when viewed from the side of afirst surface facing a visual target.

A thick solid curve M--M' is shown on each of the lenses 71 and 72. Thiscurve M--M' is obtained by connecting the passing positions of thefixation line of the corresponding eye of the lens wearer for both ofdistant vision and near vision when he views a visual target disposeddirectly in front of him. Thus, this curve M--M' coincides normally withthe aforementioned umbilical meridian curve.

A straight line L--L' is also shown on each of the lenses 71 and 72.This line L--L' extends vertically through the passing positions of thefixation line of the associated eye of the lens wearer for distantvision and is called the meridian curve.

A line S--S' is also shown on each of the lenses 71 and 72. This lineS--S' is obtained by vertically connecting the passing positions of thefixation line of the associated eye of the lens wearer when the fixationline is diverted toward the right through an angle of 45°.

When the lens wearer views, through the ophthalmic lenses shown in FIG.7, a visual target disposed at a finite distance in front of him, thetwo eyes converge more or less, and the fixation lines pass on theumbilical meridian curves M--M' instead of the meridian curves L--L'.Suppose that this visual target moves away progressively rightward inthe horizontal direction. Then, the fixation lines move progressivelyrightward through an angle of 45° until finally they pass on the linesS--S' described above. In the course of the above manner of fixationline movement, the moving distance of the fixation line of the right eyeon the associated ophthalmic lens is longer than that of the left eye.Conversely, the moving distance of the fixation line of the left eye islonger than that of the right eye when the visual target moves awayprogressively leftward in the horizontal direction. Thus, when both ofthese two cases are considered, it can be concluded that the movingdistance of the fixation line of each of the eyes on the associatedophthalmic lens is longer on the temporal side than on the nasal sidewhen the lens wearer viewing with the two eyes a visual target disposedat a finite distance in front of him diverts the eyes laterally in thehorizontal direction for binocular lateral vision. It is preferable thatthe lens 71 for the left eye and the lens 72 for the right eye are inthe form of mirror images of each other, that is, they are symmetricalwith each other on opposite sides of the nose.

It is also preferable that the fixation lines of the two eyes forbinocular vision pass on the ophthalmic lenses at such positions atwhich the factors of refraction (mean refractive power, amount ofastigmatism, directions of major axes of astigmatism, etc.) with respectto one of the eyes are approximately equal to those with respect to theother.

Therefore, it is preferable that the distributions of the factors ofrefraction in the ophthalmic lenses 71 and 72 shown in FIG. 7 are mirrorimages of each other; that the factors of refraction in each of thelenses 71 and 72 are so distributed as to be symmetrical with each otherrelative to the meridian curve L--L' in the horizontal direction in theregion where the umbilical meridian curve M--M' overlaps the meridiancurve L--L'; and that the factors of refraction in each of the lenses 71and 72 change more gradually in the horizontal direction on the temporalside than on the nasal side in the region where the umbilical meridiancurve M--M' is displaced more or less toward the nasal side relative tothe meridian curve L--L'. It is also preferable that the factors ofrefraction in each of the lenses 71 and 72 are symmetrical with eachother relative to the meridian curve L--L' in the zones spaced apart bya "predetermined distance" of, for example, 15 mm from the meridiancurve L--L' in the horizontal direction. This "predetermined distance"can be determined for each of individual points on the curve L--L'.

A preferred embodiment of the present invention will now be described.Referring to FIG. 7, the left-eye ophthalmic lens made according to thepresent invention is generally designated by the reference numeral 71,and the view is taken from the side of a visual target.

A point O is the geometrical center of the lens 71, and another point Nshown on the lens surface is located beneath the center O at a positionspaced apart by a vertical distance of 14 mm from the horizontal linepassing through the center O and a horizontal distance of 2.5 mm towardthe nasal side from the meridian curve L--L'.

In the illustrated lens 71, the area upper than the horizontal linepassing through the point O serves as the region for distant vision, andthe area lower than the horizontal line passing through the point Nserves as the region for near vision. The remaining area, that is, thearea lower than the horizontal line passing through the point O andupper than the horizontal line passing through the point N provides theregion for intermediate vision. The line L--L' represents theaforementioned meridian curve passing through the point O, and the curveM--M' represents the aforementioned umbilical meridian curve passingthrough both of the point O and the point N. The distribution ofrefractive power on this umbilical meridian curve M--M' is such that therefractive power on the portion M-O has a constant value D_(F), therefractive power on the portion N-M' has a constant value D_(N), and therefractive power on the portion O-N increases progressively from D_(F)to D_(N). The straight lines S--S' and T'T' are located in a relationparallel and symmetrical with respect to the meridian curve L--L', andthe horizontal distances from the meridian curve L--L' are equal to eachother or 23 mm in the preferred embodiment of the present invention. Theregions outer relative to the straight lines S--S' and T--T' provideplanes symmetrical with each other relative to the meridian curve L--L'in the horizontal direction.

The shape of the surface of the lens 71 according to the presentinvention is defined by an envelope of a group of sectional curves whenthe lens is sectioned in the horizontal direction by planes passingthrough a plurality of arbitrarily selected points Gi on the umbilicalmeridian curve M--M'.

As described hereinbefore, the radius of curvature of each individualcurve at the point Gi is so determined that the point Gi provides theumbilic. An arc will be the simplest form of the sectional curve. Infact, the initially employed form of the sectional curve was an arc inthe embodiment of the present invention, and the shape of the sectionalcurve was modified by taking into account the distribution of thefactors of refraction (.[.means.]. .Iadd.mean .Iaddend.refractive power,amount of astigmatism, directions of major axes of astigmatism, etc.)described later. In this connection, the radius of curvature at thepoint Gi is preferably excepted from the modification so as to maintainthe function of the point Gi as the umbilic. To find the two major radiiof curvature and their axial directions at an arbitrarily selected pointon an envelope of provisionally determined sectional curves in a manneras described above is well known as the Gauss' differential theory ofsurfaces.

The two major radii of curvature can be converted into the refractivepower, whose unit is the diopter, by the following equation well knownin this field of art:

    D=(N-1)/R

where D is the refractive power whose unit is the diopter, R is theradius of curvature whose unit is the meter, and N is the index ofrefraction of the lens, having no unit. The arithmetic .[.means.]. meanof the two values of the refractive power thus calculated gives the meanrefractive power, and the difference therebetween gives the amount ofastigmatism. The axial directions of astigmatism coincide with the axialdirections of the major radii of curvature above described. After thecalculation of the distribution of the factors of refraction in themanner above described, the shape of the surface of the lens 71 isdetermined by modifying the factors of refraction in such a manner thatthe factors change .[.less.]. .Iadd.more .Iaddend.gradually from theumbilical meridian curve M--M' toward the temporal side in thehorizontal direction than from the umbilical meridian curve M--M' towardthe nasal side in the horizontal direction in the region where theumbilical meridan curve M--M' is displaced more or less toward the nasalside relative to the meridian curve L--L', as described already. Whilethe lens 71 for the left eye has only been referred to in detailhereinbefore, it is apparent that the same applies also to the lens 72for the right eye.

Thus, the both sides of spectacles 71 and 72 can be shaped to have thevisual-target viewing surfaces which are mirror images of each other.That is, their lens surface configurations are the same in the regionprovided for distant vision and are symmetrical with each other in theregions provided for intermediate vision and near vision. Thedistribution of the factors of refraction at the surface of the lens 71for the left eye shown in FIG. 7 is such that the values of refractivepower on curves T₁ --T₁ ', T₂ --T₂ ', T₃ --T₃ ' and T₄ -T₄ ' depicted onthe temporal side are approximately equal in the horizontal direction tothose of corresponding curves S₁ --S₁ ', S₂ --S₂ ', S₃ --S₃ ' and S₄--S₄ ' depicted on the nasal side, respectively. The same applies alsoto the lens 72 for the right eye. At a glance on FIG. 7, it will bereadily seen that, in the region in which the umbilical meridian curveM--M' is more or less displaced toward the nasal side relative tomeridian curve L--L' in each of the lenses 71 and 72, the factors ofrefraction change .[.less.]. .Iadd.more .Iaddend.gradually in theportion closer to the temporal side relative to the umbilical meridiancurve M--M' than the portion closer to the nasal side relative to theumbilical meridian curve M--M'. The lens surface designed according tothe present invention can be formed on a piece of suitable lens materialby any one of suitable methods employed hitherto in this field of art.

By way of example, the lens surface according to the present inventionmay be divided into a matrix of 0.5 mm×0.5 mm squares, and the data ofcutting depths at the individual intersections may be stored in a memoryprovided for a numerically-controlling milling machine, the lensmaterial being then cut with the milling machine so as to obtain arelatively rough lens surface. The relatively rough lens surface maythen be ground with a sheet of soft grinding cloth, followed bysuccessive steps of polishing with abrasives of gradually reduced grainsizes, until finally the desired completely polished lens surface can beobtained.

What is claimed is:
 1. An ophthalmic lens having two refractivesurfaces, one of said refractive surfaces including an imaginary firstmeridian curve (M--M') called an umbilical meridian curve extendingsubstantially in the vertical direction along said refractive surfacewhen said refractive surface is viewed from a direction substantiallyorthogonal with respect thereto in the condition in which said lensstands in the same vertical direction as that mounted on a wearer, thedistribution of the radius of curvature of said umbilical meridian curve(M--M') including a zone in which the radius of curvature decreasesgradually from an upper portion toward a lower portion of said curveaccording to a predetermined rule, the radii of curvature at theintersections of orthogonal curves crossing at right angles with saidumbilical meridian curve (M--M') in said refractive surface beingsubstantially equal to the radii of curvature of said umbilical meridiancurve (M--M') at said intersections respectively so that the astigmatismalong said umbilical meridian curve (M--M') in said refractive surfaceis almost equal to zero, said umbilical meridian curve (M--M') dividingsaid refractive surface into two lateral areas closer to the nasal sideand temporal side respectively when said lens is mounted on the wearer,said two lateral areas of said refractive surface being asymmetricalwith each other, said refractive surface being such that, when a secondmeridian curve (L--L') .[.extendiang.]. .Iadd.extending .Iaddend.in thevertical direction along said refractive surface to overlap, intersector contact with said umbilical meridian curve (M--M') in an upper regionof said refractive surface is imagined, said umbilical meridian curve(M--M') is displaced toward the nasal side relative to said secondmeridian curve (L--L') in a lower region of said refractive surface,while it is .[.less.]. gradually displaced toward the nasal siderelative to said second meridian curve (L--L') in an intermediate regionof said refractive surface, said intermediate and lower regions in whichsaid umbilical meridian curve (M--M') is displaced more or less towardthe nasal side relative to said second meridian curve (L--L') includingat least one sectional curve which extends in the horizontal directionwithin a range of not more than 15 mm on opposite sides of saidumbilical meridian curve (M--M') and along which the distribution ofastigmatism on the nasal side relative to said umbilical meridian curve(M--M') is asymmetrical with that on the temporal side.
 2. An ophthalmiclens having two refractive surfaces, one of said refractive surfacesincluding an imaginary first meridian curve (M--M') called an umbilicalmeridian curve extending substantially in the vertical direction alongsaid refractive surface when said refractive surface is viewed from adirection substantially orthogonal with respect thereto in the conditionin which said lens stands in the same vertical direction as that mountedon a wearer, the distribution of the radius of curvature of saidumbilical meridian curve (M--M') including a zone in which the radius ofcurvature decrease gradually from an upper portion toward a lowerportion of said curve according to a predetermined rule, the radii ofcurvature at the intersections of orthogonal curves crossing at rightangles with said umbilical meridian curve (M--M') in said refractivesurface being substantially equal to the radii of curvature of saidumbilical meridian curve (M--M') at said intersections respectively sothat the astigmatism along said umbilical meridian curve (M--M') in saidrefractive surface is almost equal to zero, said umbilical meridiancurve (M--M') dividing said refractive surface into two lateral areascloser to the nasal side and temporal side respectively when said lensis mounted on the wearer, said two lateral areas of said refractivesurface being asymmetrical with each other, said refractive surfacebeing such that, when a second meridian curve (L--L') extending in thevertical direction along said refractive surface to overlap, intersector contact with said umbilical meridian curve (M--M') in an upper regionof said refractive surface is imaged, said umbilical meridian curve(M--M') is displaced toward the nasal side relative to said secondmeridian curve (L--L') in a lower region of said refractive surface,while it is .[.less.]. gradually displaced toward the nasal siderelative to said second meridian curve (L--L') in an intermediate regionof said refractive surface, said intermediate and lower regions in whichsaid umbilical meridian curve (M--M') is displaced more or less towardthe nasal side relative to said second meridian curve (L--L') includingrefractive surface portions which are symmetrical with each otherrelative to a plane including said second meridian curve (L--L') andwhich are included in two lateral areas spaced apart by not less than17.5 mm from said second meridian curve (L--L') in the horizontaldirection respectively.
 3. An ophthalmic lens as claimed in claim 1 or2, wherein the astigmatism along said umbilical meridian curve (M--M')is not less than zero but not more than 0.25 diopters. .Iadd.
 4. Anophthalmic lens according to claim 1, wherein the distribution ofastigmatism changes more gradually in the horizontal direction on thetemporal side than on the nasal side in the region where the umbilicalmeridian curve (M--M') is displaced toward the nasal side relative tothe meridian curve (L--L').